To document is to record. Documentary photography, therefore, can be defined as the practice of photography that is based on the idea that the photograph is a record.
As a record, the photograph gets its authority from, among others, what is called the pro-photographic event (the event was there; it happened) effect and I was there (the photographer) effect. Furthermore, it also gets its authority from the sense of authenticiy it derives from what is called the indexical effect of conjectures of cirumstance. A photograph, in other words, is a "meeting place" or rendesvous of things such as the subject matter, framing, light, characteristics of the lens, the chemical and/or digital processing, etc.
Summarized from Wells, Liz (ed.) (2004) Photography: A Critical Introduction (3rd Ed.), London: Routledge, pp. 17 - 18.